On the diophantine equation xp - x = yq - y.
Mignotte, Maurice ; Petho, Attila
Publicacions Matemàtiques, Tome 43 (1999), p. 207-216 / Harvested from Biblioteca Digital de Matemáticas
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We consider the diophantine equation

(*)    xp - x = yq - y

in integers (x, p, y, q). We prove that for given p and q with 2 ≤ p < q, (*) has only finitely many solutions. Assuming the abc-conjecture we can prove that p and q are bounded. In the special case p = 2 and y a prime power we are able to solve (*) completely.

Publié le : 1999-01-01
DMLE-ID : 3886 
@article{urn:eudml:doc:41357,
     title = {On the diophantine equation xp - x = yq - y.},
     journal = {Publicacions Matem\`atiques},
     volume = {43},
     year = {1999},
     pages = {207-216},
     mrnumber = {MR1697521},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41357}
}

Mignotte, Maurice; Petho, Attila. On the diophantine equation xp - x = yq - y.. Publicacions Matemàtiques, Tome 43 (1999) pp. 207-216. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41357/